Do you remember when President Jimmy Carter was attacked by a rabbit while fishing in 1979? Carter became the butt of many jokes about this incident. Here's a puzzle from John Tierney based on the incident:
What is your answer? The first correct answer wins a kiss from Alex.
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Suppose, the day after attacking President Carter, the rabbit finds itself alone in the middle of the pond, which is perfectly circular. Suppose there is a single Secret Service agent on the edge of the pond, armed with a small net to ensnare the swimming rabbit as it approaches the edge. This net is effective only if the rabbit is still in the water. If the rabbit reaches any point on the edge before the agent does, it can hop away to freedom; if the agent gets there first, the rabbit will be captured.
If the agent runs four times as fast as the rabbit swims, can the rabbit escape? If so, how?
For extra credit: What’s the fastest the agent can run (as a multiple of the rabbit’s speed) such that the rabbit can still escape?
What is your answer? The first correct answer wins a kiss from Alex.
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Comments (32)
So to beat the man, the rabbit needs to do more work than that. Kinda thinking a spiral pattern might work but I'm too lazy to do that math.
Let's try something simpler. If the rabbit can get himself sufficiently far in one direction, while forcing Secret Service man to be 180 degrees opposite, from there he clearly can win the race. If the pond has radius r, and the rabbit is x away from the center, then a straight swim to the edge is distance (r-x), in which time the man can run 4(r-x) and has to cover pi*r distance. So the rabbit has to be within pi*r/4 of the shore, or almost 1/4 of the way to the shore or closer, to win. The remaining question is can the rabbit get to that point, and force Secret Agent Man to the diametrically opposite side?
Well, rabbit swims 1/4 as fast as Man can run. So if rabbit is anywhere closer to the center than r/4, he can begin to swim in a circle and cover the angle faster than the man can run, and therefore swim in that circle until he forces man to be 180 degrees opposite. Then he can bolt for the shore, and to Rabbit Freedom.
So rabbit can swim to some point in between r/4 from the center and (1 - pi/4)r from the center. Regardless where the man is, Rabbi can then begin swimming his loop until the man is 180 opposite, then dash.
Ha!
"The rabbit would be able to swim from the center to the south edge in 2 seconds, while the agent would only be able to run from the north end to the south end in 3.14 seconds."
Actually the agent would be able to get from the north end to the south end in 1/2(pi) seconds; with a 2-meter radius, the pond's circumference is 4(pi), so half that is 2(pi). At 4 meters/second, 2(pi) meters would take about 1.57 seconds, and he would get there 0.43 seconds before the rabbit does.
But what was the question?
This is one of those ideas that makes you think "neat!" at first (even I did), but after considering it, I can't come up with a problem this solves.
And to answer ChuckBlack's question, I don't believe the ring above spirals all the way around like most keyrings; it's just split at the top and overlaps partway.
The ring in keyrings is made from steel and the key is made from brass, the join between the two will be a weakpoint that will hold up for a comparably short time compared to a regular key. Even if it was all made from brass it would become a weak point which would significantly lower the lifespan of the key.
Sure, if you like standing there with a snapped of key in your front door then go ahead and invest in this.
You couldn't torque the key in a bad lock.
Neat idea - but fails to solve a real problem.
Stupid concept.
Assume that this idea gains traction, and eventually all keys used by human kind sport this feature.
So then what happens when all your keys have that built-in keyring?
What do you put the keys on then?
Each other?
Or does the universe just implode into a giant singularity extinguishing all life as we know it?
Some things shouldn't be trifled with in the Natural Order of Things.